That's the one I was thinking of. Some reason I thought it was a 243. Still a weakling caliber considering how tough these animals are suppose to be.
I shot a cow in the face with a .22-250 3 or 4 years ago. I think just about anything can be killed with anything, in the right scenario with the right shooter and shot.
From my experience, nilgai can be killed with calibers much smaller than the ones you've listed. I would say .350 because of the load associated with it: we've killed 2 nilgai with 150gr .30-06 factory rounds (which are labelled at 2900fps) and they died pretty dead. One was killed with TTSX, the other with Fusion. A 200gr TTSX at that velocity sounds really good for a big blue bull.
I think your best bet would be to ask someone who kills em for a living. The exotic hunting section has a few reputable outfitters.